Dam break Reynolds number

CRI_CFD · January 20, 2020, 08:30

Which is the most suitable definition for Reynolds number in a dam break problem?

I saw things like

Re=(H*sqrt(g*H))/nu

where H is column height.

But not sure. The characteristic velocity is not known a priori...

How can I define it in terms of water column height, viscosity or related quantities?

Thanks in advance.

LuckyTran · January 20, 2020, 13:35

There isn't a velocity in Re=(H*sqrt(g*H))/nu. What's the issue? This is also a pretty good Re to use.

CRI_CFD · January 21, 2020, 07:04

Hi Lucky,

Thanks for your answer. Just wanted to verify this a suitable Re number.

I guess the same applies for Mach number (considering sqrt(g*H) as characteristic velocity), isn't it?

Thank you all for your answers.

LuckyTran · January 21, 2020, 11:49

sqrt(g*H) is the gravitational force, which is the driver and why it's a good parameter to use in your non-dimensional grouping. Re=(H*sqrt(g*H))/nu isn't really a Reynolds number. I'm just saying that it's a good non-dimensional number to use that characterizes the dam-break problem a priori. I did not mean to imply that sqrt(g*H) is a "characteristic velocity."

The three most important forces in the dam-break problem is the gravity force, surface tension, and viscous forces. The resultant velocity field will (mostly) depend on the relative strengths of those 3. So yeah it's tough to find a traditional Reynolds number.

CRI_CFD · January 22, 2020, 11:33

Thanks for your kind reply.

The situation is that I am working in Lattice-Boltzmann and the Reynolds must be conserved between physical units and lattice units (keeping Mach number low to avoid compressibility errors).

That's the reason I need to clarify the Reynolds and Mach numbers in both spaces.

Typical examples are easy to understand (flow past a cylinder, lid-driven cavity...). Characterisitc lenghts and velocities are straightforward, but I am not sure how to deal with this in a dam break (or any other problem where it is not mentioned the flow characteristic velocity).

Any ohter detail will be really appreciated.

Regards

January 20, 2020, 08:30	Dam break Reynolds number	#1
CRI_CFD Member Richardpluff Join Date: May 2014 Posts: 95 Rep Power: 12	Which is the most suitable definition for Reynolds number in a dam break problem? I saw things like Re=(Hsqrt(gH))/nu where H is column height. But not sure. The characteristic velocity is not known a priori... How can I define it in terms of water column height, viscosity or related quantities? Thanks in advance.

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January 20, 2020, 13:35		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,747 Rep Power: 66	There isn't a velocity in Re=(Hsqrt(gH))/nu. What's the issue? This is also a pretty good Re to use.

January 21, 2020, 07:04		#3
CRI_CFD Member Richardpluff Join Date: May 2014 Posts: 95 Rep Power: 12	Hi Lucky, Thanks for your answer. Just wanted to verify this a suitable Re number. I guess the same applies for Mach number (considering sqrt(g*H) as characteristic velocity), isn't it? Thank you all for your answers.

January 21, 2020, 11:49		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,747 Rep Power: 66	sqrt(gH) is the gravitational force, which is the driver and why it's a good parameter to use in your non-dimensional grouping. Re=(Hsqrt(gH))/nu isn't really a Reynolds number. I'm just saying that it's a good non-dimensional number to use that characterizes the dam-break problem a priori. I did not mean to imply that sqrt(gH) is a "characteristic velocity." The three most important forces in the dam-break problem is the gravity force, surface tension, and viscous forces. The resultant velocity field will (mostly) depend on the relative strengths of those 3. So yeah it's tough to find a traditional Reynolds number.

January 22, 2020, 11:33		#5
CRI_CFD Member Richardpluff Join Date: May 2014 Posts: 95 Rep Power: 12	Thanks for your kind reply. The situation is that I am working in Lattice-Boltzmann and the Reynolds must be conserved between physical units and lattice units (keeping Mach number low to avoid compressibility errors). That's the reason I need to clarify the Reynolds and Mach numbers in both spaces. Typical examples are easy to understand (flow past a cylinder, lid-driven cavity...). Characterisitc lenghts and velocities are straightforward, but I am not sure how to deal with this in a dam break (or any other problem where it is not mentioned the flow characteristic velocity). Any ohter detail will be really appreciated. Regards